Brazil's president Dilma Rousseff has sought to defuse massive protests sweeping the country over the rising costs of living, acknowledging the need for better public services and more responsive government.

Hundreds of thousands of Brazilians have staged some of the biggest nationwide protests in 20 years, with widespread concerns about the bills being run up from next year's World Cup and the staging of the 2016 Olympics in Rio de Janeiro.

The protests began over small increases to bus fares and quickly became known as the '20-cent revolution'. The fare increases are significant in a country where the minimum wage is about $11 a day.

But the demonstrators' grievances quickly broadened.

Key points:

Up to 250,000 protest over rising cost of living

Protests started over jump in bus fares

Grievance's spread to concern over cost of hosting World Cup and Olympics

President Dilma Rousseff welcomed protests but condemned violence

Officials in several key cities move to cut bus fares in bid to ease tensions

Many of the young protesters are upset about rising costs of public services, often perceived as being of poor quality, and that billions of dollars are being spent on sport, rather than healthcare and education.

Brazil is spending billions of dollars hosting the Confederations Cup - which is being played currently - and the World Cup next year. Some reports place the amount as high as $15 billion.

"The government spent 1 billion Brazilian real ($485 million) on the renovation of the Maracana Stadium. The society starts to query about it, since we still have not enough investment in education and medical care," one protester said.

"I have to queue up for a long time whenever I go to hospital ... my family has to pay a lot of money for my brother to go to school. That's ridiculous," another protester said.

More than 200,000 people took place in protest marches

Speaking the morning after more than 250,000 Brazilians marched in more than half a dozen cities, the president said her government remained committed to social change and was listening attentively to the many grievances expressed at the demonstrations.

"Brazil woke up stronger today," Ms Rousseff said in a televised speech in the capital, Brasilia.

"The size of yesterday's demonstrations shows the energy of our democracy, the strength of the voice of the streets and the civility of our population.

"The voices from the streets need to be heard. They transcend the traditional mechanisms of institutions, of political parties, of class and the media," the former left-wing activist, who faces re-election next year, added.

"Those who took to the streets yesterday gave a direct message to the entire society and above all the government at every level."

"That direct message from the streets was for better schools, for better hospitals and for health benefits and for the right of the people to participate."

Protests continue into second day, clashes with police in Rio

An estimated 50,000 people, according to the polling institute Datafolha, had returned to the streets in Sao Paulo, Brazil's economic capital, for a second day to denounce waste, corruption and higher public transport fares.

They are the latest in a flurry of protests over the past two weeks.

Protest organisers have been at pains to keep the demonstrations peaceful, saying violence or property damage will only hurt their cause.

But there have been clashes with police in Rio de Janeiro where a handful of people tried to break into the state assembly building.

There have also been smaller scuffles with the authorities in Brazil's other cities.

"We should strongly condemn and forbid these acts of violence," Ms Rousseff said.

"We know as a government and a society that all acts of violence are destructive, shameful and only provoke more violence."

Protests are the first large-scale show of dissent since early 1990s

The protests, organised mostly by university students through snowballing social media campaigns, mark the first time Brazilians have taken to the streets on such a large scale since economic volatility and a corruption scandal led to the toppling of president Fernando Collor de Mello in the early 1990s.

Eager to ease tensions and prevent future protests, officials in at least five cities, including important state capitals such as Porto Alegre and Recife, announced plans on Tuesday (local time) to lower bus fares.

Sao Paulo Mayor Fernando Haddad, a prominent figure in Ms Rousseff's left-leaning Workers Party, said in a meeting with leaders of the protest movement on Tuesday that he is considering a cut in bus fares but needs to find ways to compensate for the loss in revenue.

Ms Rousseff travelled to Sao Paulo on Tuesday afternoon to meet with Haddad and former president Luiz Inacio Lula da Silva, her predecessor and political mentor.

The former metalworker and union boss, who led massive protests in the late 1970s, remains an important power broker in Brazilian politics.

The unrest comes at a delicate time for Rousseff, whose administration is struggling to rein in high inflation and get the economy back on track after two years of sluggish growth.

Polls show Ms Rousseff remains widely popular, but her approval ratings have begun to slip in recent weeks for the first time since taking office in early 2011.